Final answer:
Ahmed Shah Durrani's sixth invasion of India occurred in 1761, with the Battle of Panipat marking its culmination. The date is not listed in the given options, but it is historically significant as it played a pivotal role in shifting the power dynamics of the Indian subcontinent.
Step-by-step explanation:
Ahmed Shah Durrani, also known as Ahmad Shah Abdali, invaded India multiple times in the mid-18th century to expand his territory. His invasions played a significant role against the backdrop of the declining Mughal Empire and the rise of European colonialism and control in India. Ahmed Shah Durrani's sixth invasion of India took place in the year 1761, which culminated in the Battle of Panipat.
Although this date is not listed in the provided options, it is important to provide accurate historical information. The closest date to the sixth invasion in the given options is 1762 (a), but the actual battle that marked the culmination of this campaign was fought on January 14, 1761.